High speed objective lens with anastigmatically flattened field



Aug. 12, 1958" .A. w. TRQNNIER 2,846,923

HIGH SPEED OBJECTIVE LENS WITH ANASTIGMATICALLY FLATTENED FIELD FiledFeb. 25. 1957 Y'KJS i .lOf

E'ALG TAL INVENTOR ALBRECHT WILHELM TRONNIER 78.

BY M MMJZM +7 4 ATTORNEYS HIGH SPEED OBJECTIVE LENS WITH A'NASTIG-MATICALLY FLATTENED FIELD Albrecht Wilhelm Tronnier, New York, N. Y.,assignor to Far-rand Optical Co., Inc., New York, N. Y., a corporationof New York Application February 25, 1957, Serial No. 642,096

9 Claims. (CI. 88-57) Objectives of such speed have been proposed invarious forms for the purposes of photography under unfavorable lightconditions and for the imaging of objects onto the light sensitivesurfaces of television pick-up tubes. In these proposals of the priorart the objective has been corrected for the imaging of distant objects.

Similar constructions have been proposed for photography of X-ray imagescreens in which however the fine correction of image errors is effectedfor the short object distances encountered with lenses so operated atfinite conjugates. These objectives however all have only small usefulfield angles, a total field angle of some 15 being typical of the valuesachieved. These objectives of the prior art are in some cases providedwith only a single monochromatic correction, or else they have beenachromatized over only a very narrow range of wavelengths, primarily ofthe green and blue. In these designs zonal errors up to some fivethousandths of the equivalent focal length have been accepted.

Many attempts have been made to improve these previous forms ofobjective. It has however always appeared that a reduction of the zonalerrors must be achieved either at the cost of a reduction in therelative aperture or at the cost of a reduction in the useful field, orelse that upon increase in relative aperture or of the useful field thezonal errors increased on the axis as well as in the extra-axial fieldportions so that the lens performance was perceptibly reduced.

The invention in contrast provides a new constructional form for veryhigh speed objectives having a large useful field of some 30 totalwithin which all longitudinal residual aberrations for on-axis as wellas off-axis object points are reduced to less than two thousandths ofthe equivalent focal length. By means of the invention moreover it ismade possible to effect chromatic correction over a broad spectralrange.

The invention achieves this improvement by means of a new physicalarrangement of the individual elements of the lens, in particular ofthose surrounding the diaphragm position.

The invention will now be described in detail with reference to theaccompanying drawings in which:

Figs. 1 and 2 are axial sections through two forms of lens according tothe invention; and

Fig. 3 is a graph useful in explaining the properties of the lens of theinvention, in particular the lens of Example 1.

The lens of the invention comprises five components United States Patent0 2,846,923 Patented Aug. 12, 1958 each including one or more elements,i. e. one or more pieces of transparent refractive material. Thecomponents are identified in each of Figs. 1 and 2 as L to L beginningat the long conjugate side of the lens. The lens is in use usuallyfollowed by a field lens shown in Figs. 1 and 2 in dashed outline asL(F)- In each of Figs. 1 and 2 the five lens components L to L areshownin section with their individual lens elements L; to L and with thefield lens L indicated as element L As with all subscripts used in Figs.1 and 2, the numbers increase from the long to the short conjugate side.The thicknesses of the lens elements are indicated as I, to t and thespacings of the lens components L to L are identified as suyz) to 51 1whereas the axial spacings of the lens elements within the components L14(2) and L are indicated as a;, a and a The radii of curvature of thesurfaces presented to the long conjugate side of the system areidentified by the letter R with subscripts, whereas those presented tothe short conjugate side are identified by the letter R. The diaphragmis indicated at D.

Figs. 1 and 2 difier in that Fig. 1 shows the component L made up of twoair-spaced elements and shows an air spacing of components L and Lwhereas in the embodiment of Fig. 2 the two elements of L are cementedtogether. Further, in Fig. 2, the adjacent surfaces of components L andL are cemented together.

Referring to Figs. 1 and 2 the diaphragm space is limited on the longconjugate side of the lens by a concave negative meniscus componentpreferably including two elements L and L as shown. On the side of theshort conjugate a likewise concave negative meniscus component L ispresented to the diaphragm position. This is directly followed by adispersing component L having unequal surface curvatures and having ahigh power. Consequently in the objectives of the invention thediaphragm space is surrounded by three overcorrecting divergent lenscomponents.

By this concentration of overcorrecting effect in the immediateneighborhood of the diaphragm the invention makes possible theachievement of a fine correction over a substantially larger field thanhitherto. The invention also permits a much greater reduction of theaperture aberrations within this large field than do the lens forms ofthe prior art in which only one, or at most two divergent componentswere provided in the vicinity of the diaphragm.

Another characteristic feature of the invention comprises theattribution to these divergent components of such a distribution ofpowers as to permit achievement of the desired overcorrections, withoutthe use of such large negative powers as to reduce the speed of thesystem or to require for compensation thereof the use in other systemcomponents of very high positive powers, which have undesirable effectson the form and distribution of the zonal errors.

The power relations among the various components, elements and surfacesof the lens will be given in terms of a power symbol f for theequivalent total power of the lens and in terms of a power symbol Asubscript in parentheses to the power symbol 4) denotes a power sum, i.e. the sum of the powers of the surfaces of the component identified bythe subscript, if Arabic, or the sum of the powers of the surfaces ofthe element identified by the subscript if Roman. Similarly p denotesthe surface power sum of the field lens. -An Arabic subscript, not inparentheses, to the power symbol denotes the power of an individualsurface, the subscript being applied to the primed power symbol in thecase of surfaces presented to the short conjugate side of the system andbeing applied to the unprimed power symbol in the case of surfacespresented to the long conjugate side of the system.

In accordance with the invention the distribution of powers among thethree divergent components L and L is made as follows:

(1)- The sum m of the surface powers of the two exterior surfaces R andR'.; of the negative meniscus component L disposed on the long conjugateside of the diaphragm space with its concave surface thereto lies inabsolute value between 80% and 160% of the equivalent total power of theobjective.

(2) The sum o of surface powers of the negative meniscus component Lfollowing the diaphragm position, likewise having its concave side tothe diaphragm, lies in absolute value between 30% and 80% of theequivalent total power of the objective.

(3) These two negative meniscus components L and L are so proportionedthat the sum 41 of the surface powers of the two concave surfaces R, andR thereof adjacent the diaphragm space possesses an absolute valuebetween 250% and 450% of the equivalent total power of the objective.

(4) The sum of the surface powers of the divergent component L ofunequal surface curvatures which follows the negative meniscus componentL on the rear side of the diaphragm space possesses an absolute valuebetween 130% and 260% of the equivalent total power of the objective.

This central group of three lens components L L(3) and L is enclosed onboth sides by a convergent component, the component L on the shortconjugate side having substantially greater power than the com ponent Lon the long conjugate side. These exterior lens components are accordingto the invention so proportioned that:

(1) The sum of the powers of all surfaces of the component L liesbetween 50% and 130% of the equivalent total power of the objective.

(2) The sum of the powers of all the surfaces of the component L liesbetween 300% and 600% of the equivalent total power of the objective.

The new objective of the invention thus possesses the following make-up,beginning at the long conjugate end thereof:

(1) A convergent two-element front component L whose surface power sumge is related to the equivalent power a: of the objective by therelation (2) A negative meniscus component, L concave toward thediaphragm which follows it, advantageously made up of two individuallenses L and L for purposes of spherochromatc correction. The surfacepower sum m of its two exterior surfaces R and R1,, both concave towardthe diaphragm, conforms to the relation (3) The diaphragm space islimited on the short conjugate side by a divergent meniscus component Lconcave toward the diaphragm space. The two divergent lens surfaces R.;and R which limit the diaphragm space possess a surface power sum Wconforming to the relation (4) This negative meniscus component L is soproportioned that the sum of its surface powers conforms to the relation(5) Then comes a strongly divergent negative component L of unequalcurvatures whose surface power: sum 95 conforms to the relation (:3)Lastly comes a strongly convergent component. I so proportioned that thesum of its surface powers conforms to the relation I or a negativelycurved image surface according as there is desired a plane image, forexample for photographic purposes, or a curved image surface, as intelevision tubes.

Usually, in view of its location close to the final image surface, sucha field lens takes the form of a single lens element of divergent power.It can however according to the intended use of the objective comprisetwo elements and may be of other than negative power, or it can comprisean element of nonspherical power, prismatic for example. Its physicalform is specified less by the objective of the invention than by theparticular application intended.

This make-up of the objective of the invention makes possibleachievement of an extremely fine imagery out to and beyond average fieldangles at very high relative aperture values, up to and beyond f/ 0.9.Objectives of this class of speeds have on the image side only a veryshort depth of focus because of the large angle of the cones or bundlesof rays encountered. Hence for practical use of wide field angles theachievement of a particularly good anastigmatic imagery is of particularsignificance by comparison with systems of normal speed and aperturevalues.

In the case of the present objectives, which constitute a furtherimprovement of the modified Gaussian type,

the pair of adjacent surfaces R' and R of components L and L is madestrongly convergent so that the sum of the powers of these surfaces,which may be written as (4 5) or as 1p lies between 12.5% and 47.5% ofthe equivalent total power of the objective. Thus:

Adherence to this criterion of the invention makes possible a verycomplete reduction in the difierence between the sagittnl and meridionalimage surfaces in the lateral portions of the field.

Within a field thus nearly free of astigmatism, particular attentionmust be paid to reduction of the comatic errors of wide-angle raybundles if the desired fine imagery is to be achieved with bundles offull angular aperture.

Here the invention provides a startlingly effective and simple way toachieve an imagery largely free of asymmetry errors. As between the twostrongly convergent individual elements L and L of the convergentcomponent L the element L is provided with a stronger positive powerthan the element L in accordance with the following rule:

qs and qswm) being respectively the sums of the powers of the surfacesof elements L and L This,

possesses a stronger power than the preceding front element L asfollows:

and rp being respectively the sums of the powers of the surfaces of theelements L and L The new objectives according to the invention makepossible a realization of these improvements without requiring the useof radii which are difiicult to produce, for example by reason of sharpcurvatures. Neither do the objectives of the invention require the useof crystalline materials for the lens elements. On the contrary theobjectives of the invention may be realized with the customary glassesof commerce as the examples presently to be given will show. As regardsglasses there is selected for both of the high power convergent elementsL and L behind the diaphragm a glass of high index such as one of themodern glasses low in silica. This choice is made in order to permitrelatively flat surfaces in spite of the high surface powers required.Beyond this there are employed only the usual crown and flint glasseswhich are used in much slower objectives. according to the invention therelative apertures of both of which are greater than f/ 0.9 and whichare therefore to be regarded as extremely fast anastigmats, since theyare provided with a true suppression of the difference between sagittaland meridional image surfaces in the extra axial portions of the field.

In the tabular data for the examples the glasses are identified withrespect to their index of refraction n (for the d line of helium havinga wavelength of 5876 Angstrom units) and with respect to theirdispersion in terms of their Abbe number v.

EXAMPLE 1 This example presents for an assumed focal length 1 of 100millimeters, corresponding to an equivalent total power I of diopters,the following basic power distribution:

Table 1 Diaphragm space:

=-37.8 dptr.

The relative aperture of the lens of Example 1 is f/ 0.88 and its usefulfield is In terms of the equivalent total power I the distribution ofpowers for the lens components set forth in Table 1 may be givenapproximately as follows:

If now consistently with the properties above set forth concerning therelations between qfiwn and (vm) and between 47(1) and qs oneadditionally sets:

There will now be given two examples of lenses the following furtherdistribution of powers appears for the individual elements of the lensof Example 1:

For the field lens:

(F)=- 13.5 dptr.

The basic construction implicit in the data for Example 1 already givencontains an approximate third order correction. In order to improve thisthird order correction the surface power sums set forth in Tables 1, 2and 3 are preferably achieved by an individual surface powerdistribution as follows:

Table 4 The lens of Example 1 may be constructed from commerciallyavailable glasses as follows:

Table 5 Element Glass Type Index 0 Abbe Numberv light barium crown glassm=1. 59 v1=6l dense barium crown glass m=1. 64 vz= dense barium crownglas m=1. 64 m=55 ordinary dense fiint m=1. n=30 extra dense lead fiintn =1. 73 v5=28 medium flint m=1. 64 va=35 dense lanthanum (rare-earth)glass n1=1.74 v1=45 dense lanthanum (rare-earth) gloss m=1. 74 va=45 Iordinary crown M m=l. 52 w=57 By selecting glasses of specific index anddispersion values, generally within the values set out in Table 5, oneobtains for the lens the data as set out in Table 6 below (in terms ofan assumed focal length f=1.0), it being noted that the lens thicknessesmust be dimensioned with proper regard for the large lens diameterswhich are required by the high speed of the objective, the diameter ofthe front element being required to amount to at least 115% of theequivalent focal length of the entire lens.

With power distribution given above in Table 4 and data for the lensthus becomes as follows:

An analysis of the Seidel region aberrations of the lens in accordancewith the approximate data given in Table 6 strikingly indicates theimprovements in imagery obtained in accordance with the invention andfurther shows how a further and higher degree of correction is madepossible.

The following definitive data for the lens of Example 1 show by a simplecomparison of values that with a minimum amount of computational efforton variation in values from the approximate data already given there isachievable the great improvement made possible by the invention.

Table 7 [Lens of Example l relative aperture 170.83, scale-l to a heallength of 1 mm.]

Surface Radius Thickness t or Abbe Element in mm. spacing a or 8, Indexn Number v in mm.

R =+l35. -19 L s t1=l4. 2095 m==l.58987 v|=6l.2

R' =+7Sl. 92

m=0. 5282 R;=+84. 121 L 12 14. 2095 n:=1.63909 vz=55. 5

s 1,2 =0. 7924 R;=+5-l. 052 L1 t3=24. 6289 n;=l. 63909 v3=55. 5

R' on L: v t.;= 1.529fi 7l 1. 69842 30. 1

s (2.2) =28. 4322 R: 50. 4S6 Lv i.-.=3.8825 71 :1. 72850 28.3

.1 (3,4) =1. 2942 Rs= 387. .33 Lvr ts=3. 8825 'nq=l. 63694 =35. 4

8 (4.5) =0 R. =+37. 108 Lvn 7: 19. 3730 nr= 1. 74400 v1=44. 7

0 1. 29-12 R3=+CY1J197 Lvrn 85 22. 0782 ns=1.7-1400 11 :44. 7

With a spacing s a =5.942S for the field 10115 L the lens should be asfollows:

R 64. 497 L111 t 1. 9809 m=1. 51630 vn=56. 8

ill

To these fully worked out geometrical data for the lens of Fig. 1 therecorrespond the following surface power values, correct to one part inone hundred thou sand:

Table 8 The equivalent power of the objective amounts to exactly 10diopters.

The power of each individual surface is as usual given by the formulawherein n and n are the indices of the media on the entering andemergent sides of the surface and R is the radius of curvature thereofin millimeters. The surface power sum qfiwm) of the last convergentelement L on the image side of the system amounts to +17.02645 dioptersand hence to or 60.959% of the surface power sum qS of the precedingconvergent element L The surface'power sum qb of the front element L; onthe object side amounts to +3.599l5 dptr. and hence to the equivalentfocal length f, for various principal ray inclination (n on the longconjugate side of the lens, given in the scale of ordinates at theright. The lefthand scale oi fordinates Y' gives the intersectionheights in the image plane of the principal rays, in fractional parts ofthe equivalent focal length f. Fig. 3 thus indicates the improvementachieved by the invention.

EXAMPLE 2 This objective possesses an even higher relative aperture thandoes the lens of Example 1, its numerical aperture of 0.577corresponding to a relative aperture of f/0.866. The useful field ofthis lens has a diameter somewhat more than 50% of the equivalent focallength. By application of the constructional principle of the inventionthe lens of Example 2 is provided with an unusually fine imagery overthe whole useful field, an imagery better even than that of Example 1 inspite of the application in Example 2 of several constructionalsimplifications, namely the use of the same radii and glasses for anumber of elements, which simplifies the manufacture and mounting of thelens.

Table 9 [Relative apertnref/0.866. Equivalent focal length 100 mm'.)

Surface Radius Thickness t or Abbe Element in mm. spacing s or 11 Index1: Number in mm. 11

R =+136. 247 L l =14. 28865 'ni=1. 58896 u =6l. 5

ai=0. 53118 R =+84. 5899 L lz= 14. 67641 m= 1. 63934 vg= 55. 5

s 1.2 =0. 39838 R:=+54. 3527 Lm l3=26. 08609 123:1.63934 11 :55. 5

a R4: at L v l4=3. 18706 m= 1. 69927 v =80.l

s 2.2) 28. 59059 R 50. 7672 Lv t =3. 90415 715 1. 72800 v5=28. 3

8 (3,4) =1. 30138 R =408. 209 Lvr =3. 88821 m= 1. 63598 vg=35. 6

8 (4.5) R =+38. 3377 Lvn--. t =19. 48091 n =l. 74464 u7=4-L 6 a ==l.30138 Rg=+64. 8567 Lvmnqls=23. 10619 m=1.74-164 s=4-t. 6

For a spacing s .1: =5.97574 mm, of the field lens from the last elementLvrn of the objective, the field lens Lix should pcssess the followingproperties:

Ro= 74. 1921 L11 la=1.99l91 1lv=1. 51537 vv=56. l

In the lens of Example 2 the diaphragm is disposed at a distance b=16.51960 mm. behind the vertex of the last surface R preceding thediaphragm. With the data given in Table 9, the lens of Example 2possesses the following power distribution:

Table The equivalent power of the objective amounts to exactly 10diopters.

To indicate the unusually good imagery of the lens of Example 2, thereis given in the accompanying Table ll for the lens of Example 2 thevalue of the spherical aberration 6,,, for an infinitely distant object,for a few incicident ray heights, the corresponding relative aperturesbeing also given.

Table 11 [Equivalent focal length f= mm.]

Incident Relative Aperture Ray Height '5'. in mm.

in mm.

The unusually complete suppression of the difference between thesagittal and tangential image surfaces obtainable according to theinvention is further demonstrated in the accompanying Table 12,representing the result of exact computation of the astigmatism of thelens of Example 2. In this table there are given the longitudinaldepartures from a reference plane distant 79.26000 mm. from thediaphragm plane of the sagittal and meridional image points for aninfinitely distant object for three principal ray inclinations, theserays being identified by their inclination to to the axis at thediaphragm plane and by means of the intersection heights y' thereof atthe image plane. The departures of the sagittal and the meridional ortangential image points from the reference plane are identified as a and6 respectively, and are given in millimeters to the fifth decimal place,the last digit given hence representing 1,110,000,000 of the focallength. The last line of the table gives the residual astigmatism, inmm.

Table 12 2OO0J0H 3000/0]! 350010! While the invention has been describedherein in terms of a number of preferred embodiments, numerousmodifications and variations may be made therein without departing fromthe scope of the invention itself which is set forth in the appendedclaims.

I claim:

1. A high speed optical objective lens system of modified Gaussian typecomprising, from front to back, and head of the diaphragm position, afirst convergent component L :1 first negative meniscus component L and,behind the diaphragm position, a second negative meniscus component L anegative component L; of unequal surface curvatures, and a secondconvergent component L the sums s to 4 of the powers of the outersurfaces of the said components L to L respectively being related to thetotal equivalent power i of the objective as follows:

the sum m of the powers of the rear surface of component L and of thefront surface of the component L being in addition related to the totalequivalent power rli as follows:

2. A lens system according to claim 1 in which the sum fi of the powersof the rear surface of said negative component L and of the frontsurface of said second convergent component L is related to the totalequivalent power I of the objective system as follows:

3. A lens system according to claim 1 in which said second convergentcomponent L includes a biconvex element L followed by a convex element Lthe sums qbw and of the powers of the surfaces of said elements L and Lrespectively conforming to the following relation:

4. A lens system according to claim 3 in which said first convergentcomponent L includes first and second elements L and L the sums gbu andm of the powers of whose surfaces conform to the following relation:

5. An objective lens system according to claim 1 in which the sums 45(1)to of the powers of the outer surfaces of its components L to Lrespectively are related to the equivalent total power I of theobjective system substantially as follow's:

and in which the sum m of the powers of the rear surface of component Land of the front surface of component L and the sum o of the powers ofthe rear surface of the negative component L and of the front surface ofthe second convergent component L are related to the equivalent totalpower I of the objective system substantially as follows:

6. An objective lens system according to claim 4 in which the firstnegative meniscus component L includes front and rear elements L and Lin which the second negative meniscus component L and the negativecomponent L include respectively elements L and L and in which thedistribution of the sums to qi of the powers of the surfaces of theelements L to L thereof respectively is substantially as follows:

in which the sum (2,3) of the powers of the rear surface of element Land of the front surface of element L is substantially 37.8 diopters andin which the sum' m of the powers of the rear surface of element L andof the front surface of element L is substantially +2.9 diopters.

7. A high speed optical objective system of modified Gaussian typecomprising, from front to back, two elements L and L forming a firstconvergent component, two elements L and L forming a first negativemeniscus component, a second negative meniscus element L a negativeelement L of unequal surface curvatures, and two elements L and Lforming a second convergent component, said elements conformingsubstantially to the following conditions:

Thickness t, Surface Radius Gap (1, or Element in Multiples of Spacing sin Index n Abbe the Equivalent Multiples of No. :1

Focal Length the equivalent focal length R =+L 35 f L; t =().14f m=1.590 vr=51. 2

' r=0 005 f R2=+0. 84f Lu ta=0. 14f ng=l. 639 uz=55. 5'

-?(1,2)=0. 008/' I R =+0. 54/ LHI f3=0-25f Tl3=l.639 u =55.5

R' co Iln=0 R4: at: LIV t4=0 04f m=l 698 u =30.l

sem=0 8f R =0. 51 f I Lv t =0. 04f m=L 729 v =28. 3

86.4) =0. 01 R 3. 8f Lvr f5=0- 04f 7Lu=l. 637 ue=35. 4

NM) =0 R1=+0. 37f Lvrr t1=(l. 19f n =l. 744 v7=44. 7

R1= O. 94/ l a =0. 01 f Ra=+0. 64f Lvm is=0. 23 f n =l. 744 g=44l 7 8(me f Rq=0- 64f LIX fo=0.02f 7tn=1:5l6 v9=56 8 wherein R to R arerespectively the radii of the front refracting surfaces of the elementsL to L R to R are respectively the radii of the rear refracting surfacesof the elements of L; to L 1 to t are respectively the axial thicknessesof the elements L; to L a a and a are respectively the axial gapsbetween the pairs of elements L and u, L and L L and L and s s a s s 5are respectively the axial spacings between the pairs of elements L andL1H, LIV and Lv, Lv and LVI, LVI and Lvn, LVIH and 8. A high speedoptical objective system of modified. Gaussian type comprising, fromfront to back, two elements L and L forming a first convergentcomponent, two elements L and L forming a first negative me niscuscomponent, a second negative meniscus element L a negative element L ofunequal surface curvatures, and two elements L and L forming a secondconvergent component, said elements conforming substantially to thefollowing conditions:

sum Radius Thickness t, Abbe Element in mm. Gap (1, or Spac- Index 1: o.v

lng a in mm.

R =+135. 49 L1 t =14. 2095 711 1. 58987 v =61. 2

(l1=0- 5282 Rz= +84. 121 Ln lg= 14. 2095 71z=l. 63909 ug=55. 5

s (1.2) =0. 7924 Rs= +54. 052 Lin ts=24. 6289 1Z3=L 63909 v3=55. 5

R fla= 4: an Liv =4. 5296 7L =L 69842 |q=30.1

80.1 =28. 4322 R 50. 486 Lv !s=3- 3825 m=1. 72850 v5=28.3

8 ,4 =1. 2942 Rs= 387. 33 Lv is=3. 3825 'Ilo=1. 63694 .9ug=35.4

3 (1.5) 0 R =+37. 108 Lvn t1=19.3730 n =1.74400 v1=44.7

0; =1. 2942 Ra=+64. 497 LvnI--- l3=22.9782 m=1. 74400 va=44. 7

wherein R to R are respectively the radii of the front refractingsurfaces of the elements L to L R; to R' are respectively the radii ofthe rear refracting surfaces of the elements L; to L to t arerespectively the axial thicknesses of the elements L to L a a and a arerespectively the axial gaps between the pairs Of elements LI and Lu, Lmand LIV, Lvn and LVIH; and s s av s are respectively the axial spacingsbetween the pairs of elements L and L L and L L and L L and L 9. A highspeed optical objectives system of modified Gaussian type comprising,from front to back, two elements L and L forming a first convergentcomponent, two elements L and L forming a first negative meniscuscomponent, a second negative meniscus element L a negative element L ofunequal surface curvatures, and two elements L and L forming a second convergent component, said elements conforming substantially to thefollowing conditions:

Surface Radius Thlckness t or Abhe Element in mm. Spacing s or 0 Index11 Number v in mm.

R +136. 247 L1 =14. 28865 fl =1i 58896 u =6l. 6

a1=0. 53118 R +84. 5899 Lu l'3=14. 67641 m= 1. 63934 vz= 56. 5

a 1,2) =0. 39838 Rs=+54. 3527 L1 R =26. 08609 na=1. 63934 vs=65, 6

a lla=0 R: m Lxv t4=3. 18706 711 1. 69927 -30. l

8 1, 28. 69059 R5= 50. 7672 Lv t5=3.90415 m=1.72800 -28.3

80.4 =1. 30138 Ro= -408. 209 Lvr =3. 88821 m==L 63598 35. 6

8 (4.0 R1==+38. 3377 Lvn t1=19. 48091 .m=1.74464 u1=44.6

, a;=1. 30138 Rs=+6 8567 L viii... la=23. 10619 =1. 74464 "=44. 6'

References Cited in the file of this patent UNITED STATES PATENTS1,812,717 Rudolph June 30, 1931 2,012,822 Lee Aug. 27, 1935 2,319,171Warmisham et al. May 11, 1943 2,586,866 Schade Feb. 26, 1952 2,662,447Tronnier Dec. 15, 1953 2,677,989 Tronnier May 11, 1954 FOREIGN PATENTS439,142 Great Britain NOV. 29, 1935 UNITED STATES PATENT OFFICECertificate of Correction Patent No. 2,846,923 August 12, 1958 AlbrechtWilheln lmnieF f 't g It is hereby certified that error appears in theprinted specification of the above numberedpatent requiring correctionand that the said Letters Patent should read as corrected belowh Column5, line 45, Table 1, for =+8.9 dptr. read =+8.3 dptr.; column 6, line30, Table 4, for I O.7 5 dptr. read q. =0.75 dptr.; column 11, line 7,for head read ahead; line 24, for 4 read I line 41, for 0.9 I read 0.9column 13, line 21, in the table, opposite L last column thereof, for Sv=35.4 read v =35.4; line 39, for objectives read 0bjective.

Signed and sealed this 11th day of November 1958.

[SEAL] Attest KARL H. AXLINE, ROBERT C. WATSON,

Attestz'ng Ofiaer. Commissioner of Patents.

